what is the following quotient?\n$\frac{3sqrt{8}}{4sqrt{6}}$\n$\frac{12sqrt{2}-6sqrt{3}}{5}$\n$\frac{3sqrt{6}…

Explanation:

Step1: Simplify $\sqrt{8}$

$\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$

Step2: Substitute $\sqrt{8}$ into the original expression

The original expression $\frac{3\sqrt{8}}{4\sqrt{6}}$ becomes $\frac{3\times2\sqrt{2}}{4\sqrt{6}}=\frac{6\sqrt{2}}{4\sqrt{6}}$

Step3: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{6}$: $\frac{6\sqrt{2}\times\sqrt{6}}{4\sqrt{6}\times\sqrt{6}}=\frac{6\sqrt{12}}{4\times6}$

Step4: Simplify $\sqrt{12}$

$\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}$

Step5: Substitute $\sqrt{12}$ into the expression

$\frac{6\times2\sqrt{3}}{4\times6}=\frac{12\sqrt{3}}{24}=\frac{\sqrt{3}}{2}$

Answer:

$\frac{\sqrt{3}}{2}$